Factor Rings and Splitting Ideals of Self-Injective, CS and Baer Rings

DOI10.1081/AGB-200066107zbMath1116.16001OpenAlexW2078983942MaRDI QIDQ5704499

Carl Faith

Publication date: 15 November 2005

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/agb-200066107

zbMATH Keywords

CS-ringsvon Neumann regular ringsBaer ringsright self-injective ringsregular idealsring direct summandsannihilator right idealscomplement right idealsco-nonsingular rings

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Prime and semiprime associative rings (16N60) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Ideals in associative algebras (16D25) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Cites Work

• New characterizations of von Neumann regular rings and a conjecture of Shamsuddin
• The maximal regular ideal of self-injective and continuous rings splits off
• Lectures on injective modules and quotient rings
• Self-Injective Rings
• Quasi-Injective Modules and Irreducible Rings
• RINGS IN WHICH EVERY COMPLEMENT RIGHT IDEAL IS A DIRECT SUMMAND
• A note on rings of which any one-sided quotient rings are two-sided
• Examples of Continuous Geometries
• On Regular Rings
• Note on uni-serial and generalized uni-serial rings
• Self-injective rings

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